fractal

Since everyone has a computer, the fractal is a popular curve to play with.
But what is a fractal? The name fractal is derived from the idea that the dimension of
such a curve is a fraction of an integer. Since some interesting fractal-like curves do
have an integer dimension, there is no ground left for this relationship.
However, the
name fractal persisted.
You could say that a fractal is a complex curve, for which a certain amount of similarity
can be seen, when magnifying parts of the curve.
The curves were discovered in the late 17th century, and they shocked the
mathematicians of that era.

A special case of the fractals are the space-filling
curves, curves which completely fill an area: